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Sep 19, 2013
09/13

by
Volker Schomerus

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These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are presented in the second lecture. The general formalism is then illustrated through a detailed discussion of branes on compact group manifolds. In the final lecture, many more recent developments are reviewed, including some results for non-compact target spaces.

Source: http://arxiv.org/abs/hep-th/0209241v1

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Sep 18, 2013
09/13

by
Volker Schomerus

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In this work we propose an exact solution of the c=1 Liouville model, i.e. of the world-sheet theory that describes the homogeneous decay of a closed string tachyon. Our expressions are obtained through careful extrapolation from the correlators of Liouville theory with c > 25. In the c=1 limit, we find two different theories which differ by the signature of Liouville field. The Euclidean limit coincides with the interacting c=1 theory that was constructed by Runkel and Watts as a limit of...

Source: http://arxiv.org/abs/hep-th/0306026v1

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Sep 21, 2013
09/13

by
Volker Schomerus

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During the last ten years, intriguing dualities between gauge and string theory have been found and explored. They provide a novel window on strongly coupled gauge physics, including QCD-like models. Based on a short historical review of modern string theory, we shall explain how so-called AdS/CFT dualities emerged at the end of the 1990s. Some of their concrete implications and remarkable recent progress are then illustrated for the simplest example, namely the multicolor limit of \N=4 Super...

Source: http://arxiv.org/abs/0706.1209v1

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Sep 18, 2013
09/13

by
Volker Schomerus

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In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume algebras from the operator product expansions of open string vertex operators. For branes in a flat background with constant non-vanishing B-field, the operator products are computed perturbatively to all orders in the field strength. The resulting series coincides...

Source: http://arxiv.org/abs/hep-th/9903205v1

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Sep 21, 2013
09/13

by
Henning Schomerus

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PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous PT-symmetry breaking can occur via two distinct mechanisms, whose predominance is associated to different universality classes. Present optical experiments fall into the orthogonal class, where symmetry-induced level crossings render the characteristic absorption...

Source: http://arxiv.org/abs/1011.1385v1

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Sep 18, 2013
09/13

by
Henning Schomerus

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Recent investigations address transport through ballistic charge-neutral graphene strips coupled to doped graphitic leads. This paper shows that identical transport properties arise when the leads are replaced by quantum wires. This duality between graphitic and metallic leads originates in the selection of modes with transverse momentum close to the K points, and can be extended to a wide class of contact models. Among this class we identify a simple, effective contact model, which provides an...

Source: http://arxiv.org/abs/cond-mat/0611209v2

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Sep 18, 2013
09/13

by
Henning Schomerus

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A recent paper [Jokela et al, arxiv:0806.1491 9 June 2008] contains a surmise about an expectation value in a Coulomb gas which interacts with an additional charge xi that sits at a fixed position. Here I demonstrate the validity of the surmised expression and extend it to a certain class of higher cumulants. The calculation is based on the analogy to statistical averages in the circular unitary ensemble of random-matrix theory and exploits properties of orthogonal polynomials on the unit...

Source: http://arxiv.org/abs/0806.2602v3

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Sep 18, 2013
09/13

by
Volker Schomerus

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This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of AdS/CFT-like dualities and for studies of time-dependent processes. After a general outline of the central concepts, we focus on two specific but rather prototypical models: Liouville field theory and the 2D cigar. Rather than following the historical path, the...

Source: http://arxiv.org/abs/hep-th/0509155v1

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Jul 19, 2013
07/13

by
Volker Schomerus

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It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantum symmetries and algebras of field operators. For every algebra $\A$ of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field...

Source: http://arxiv.org/abs/hep-th/9401042v1

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Jul 20, 2013
07/13

by
Henning Schomerus

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We describe an angularly asymmetric interface-scattering mechanism which allows to spatially separate the electrons in the two low-energy valleys of bilayer graphene. The effect occurs at electrostatically defined interfaces separating regions of different pseudospin polarization, and is associated with the helical winding of the pseudospin vector across the interface, which breaks the reflection symmetry in each valley. Electrons are transmitted with a preferred direction of up to 60 degree...

Source: http://arxiv.org/abs/1007.4594v2

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Sep 19, 2013
09/13

by
Henning Schomerus

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In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has a certain collective character rather than being additive in the individual periodic orbits involved....

Source: http://arxiv.org/abs/chao-dyn/9703003v1

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Sep 23, 2013
09/13

by
Henning Schomerus

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We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top.

Source: http://arxiv.org/abs/chao-dyn/9904003v1

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Sep 18, 2013
09/13

by
Henning Schomerus

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This work presents a theory of the frequency-resolved light emission of active two-dimensional dielectric microresonators, which are characterized by a highly non-paraxial mode structure and frequently feature a position-dependent dielectric constant and non-uniform gain. The Lorentzian intensity profile is characterized by an appropriately generalized Petermann factor, a renormalized peak position, and the cold-cavity resonance lifetime Gamma. The theory also delivers a relation of Gamma to...

Source: http://arxiv.org/abs/0809.2349v2

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Sep 22, 2013
09/13

by
Henning Schomerus

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The observation that PT-symmetric Hamiltonians can have real-valued energy levels even if they are non-Hermitian has triggered intense activities, with experiments, in particular, focusing on optical systems, where Hermiticity can be broken by absorption and amplification. For classical waves, absorption and amplification are related by time-reversal symmetry. This work shows that microreversibility-breaking quantum noise turns PT-symmetric systems into self-sustained sources of radiation,...

Source: http://arxiv.org/abs/1001.0539v2

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Sep 21, 2013
09/13

by
Henning Schomerus

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One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Drawing on the concepts of band-structure topology, I here describe the formation of exponentially localized, topologically protected midgap states in photonic systems with spatially distributed gain and loss. When gain and loss are suitably arranged these states maintain their topological protection and then acquire a selectively tunable amplification rate. This finds applications...

Source: http://arxiv.org/abs/1301.0777v1

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Sep 20, 2013
09/13

by
Henning Schomerus

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I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions which can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution...

Source: http://arxiv.org/abs/1207.1454v2

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Sep 24, 2013
09/13

by
H. Schomerus

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We investigate the effects of wave localization on the delay time tau (frequency sensitivity of the scattering phase shift) of a wave transmitted through a disordered wave guide. Localization results in a separation tau=chi+chi' of the delay time into two independent but equivalent contributions, associated to the left and right end of the wave guide. For N=1 propagating modes, chi and chi' are identical to half the reflection delay time of each end of the wave guide. In this case the...

Source: http://arxiv.org/abs/cond-mat/0103113v1

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Sep 20, 2013
09/13

by
Volker Schomerus

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Over the last few years, string theory has changed profoundly. Most importantly, novel duality relations have emerged which involve gauge theories of brane excitations on one side and various closed string backgrounds on the other. In this lecture, we introduce the fundamental ingredients of modern string theory and explain how they are modeled through 2D (boundary) conformal field theory. This so-called `microscopic description' of strings and branes is an active research area with new results...

Source: http://arxiv.org/abs/hep-th/0404262v1

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Aug 6, 2017
08/17

by
Friedrich Schomerus

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Topic: business management

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Sep 21, 2013
09/13

by
Henning Schomerus

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We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction...

Source: http://arxiv.org/abs/chao-dyn/9711013v1

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Jun 29, 2018
06/18

by
Henning Schomerus

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Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic Processes and Random Matrices" in July 2015, we review the physical origins and mathematical structures of the underlying models, and collect key predictions which give insight into the typical system behaviour. In particular, we aim to give an idea how...

Topics: Disordered Systems and Neural Networks, Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1610.05816

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Jul 20, 2013
07/13

by
Henning Schomerus; Jakub Tworzydlo

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In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasi-bound states is smaller than the classical time of flight. The remaining long-lived quasi-bound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91,...

Source: http://arxiv.org/abs/cond-mat/0406135v2

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Sep 19, 2013
09/13

by
Christopher Manderfeld; Henning Schomerus

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We study how the singular behaviour of classical systems at bifurcations is reflected by their quantum counterpart. The semiclassical contributions of individual periodic orbits to trace formulae of Gutzwiller type are known to diverge when orbits bifurcate, a situation characteristic for systems with a mixed phase space. This singular behaviour is reflected by the quantum system in the semiclassical limit, in which the individual contributions remain valid closer to a bifurcation, while the...

Source: http://arxiv.org/abs/chao-dyn/9911024v1

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Sep 18, 2013
09/13

by
Stefan Fredenhagen; Volker Schomerus

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In this work we study the dynamics of branes on group manifolds G deep in the stringy regime. After giving a brief overview of the various branes that can be constructed within the boundary conformal field theory approach, we analyze in detail the condensation processes that occur on stacks of such branes. At large volume our discussion is based on certain effective gauge theories on non-commutative `fuzzy' spaces. Using the `absorption of the boundary spin'-principle which was formulated by...

Source: http://arxiv.org/abs/hep-th/0012164v1

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Sep 22, 2013
09/13

by
P. Samuelsson; H. Schomerus

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We present a theory for the nonequilibrium current in a mesoscopic Josephson junction which is coupled to a normal electron reservoir, and apply it to a chaotic junction. Large sample-to-sample fluctuations of the critical current $I_{\rm c}$ are found, with ${rms} I_{\rm c} \simeq \sqrt{N}e\Delta/\hbar$, when the voltage difference eV between the electron reservoir and the junction exceeds the superconducting gap $\Delta$ and the number of modes N connecting the junction to the superconducting...

Source: http://arxiv.org/abs/cond-mat/0004197v1

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Sep 18, 2013
09/13

by
Henning Schomerus; Martina Hentschel

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We develop an amended ray optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two contributions of similar magnitude, corresponding to ray displacement in independent quantum phase space directions, which can be identified with Fresnel filtering and the Goos-Haenchen shift, respectively. Hence we unify two effects which only have been...

Source: http://arxiv.org/abs/physics/0606024v2

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Sep 23, 2013
09/13

by
Henning Schomerus; Eric Lutz

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We develop a theory describing the dynamics of quantum kicked rotators (modelling cold atoms in a pulsed optical field) which are subjected to combined amplitude and timing noise generated by a renewal process (acting as an engineered reservoir). For waiting-time distributions of variable exponent (L\'evy noise), we demonstrate the existence of a regime of nonexponential loss of phase coherence. In this regime, the momentum dynamics is subdiffusive, which also manifests itself in a non-Gaussian...

Source: http://arxiv.org/abs/0801.4497v1

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Sep 19, 2013
09/13

by
Henning Schomerus; Fritz Haake

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We determine semiclassical quasienergy spectra from periodic orbits for a system with a mixed phase space, the kicked top. Throughout the transition from integrability to well developed chaos the standard error incurred for the quasienergies is a small percentage of their mean spacing. Such fine accuracy does not even require the angular momentum quantum number $j\propto 1/\hbar$ to be large; it already prevails for $j=1,2,3$. To open the way towards a reliable spectrum the conventional trace...

Source: http://arxiv.org/abs/chao-dyn/9703016v1

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Sep 19, 2013
09/13

by
M. Titov; H. Schomerus

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We study analytically the local density of states in a disordered normal-metal wire at ballistic distance to a superconductor. Our calculation is based on a scattering-matrix approach, which concerns for wave-function localisation in the normal metal, and extends beyond the conventional semiclassical theory based on Usadel and Eilenberger equations. We also analyse how a finite transparency of the NS interface modifies the spectral proximity effect and demonstrate that our results agree in the...

Source: http://arxiv.org/abs/cond-mat/0208107v2

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Sep 21, 2013
09/13

by
Thomas Quella; Volker Schomerus

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We present a large and universal class of new boundary states which break part of the chiral symmetry in the underlying bulk theory. Our formulas are based on coset constructions and they can be regarded as a non-abelian generalization of the ideas that were used by Maldacena, Moore and Seiberg to build new boundary states for SU(N). We apply our expressions to construct defect lines joining two conformal field theories with possibly different central charge. Such defects can occur e.g. in the...

Source: http://arxiv.org/abs/hep-th/0203161v3

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Sep 23, 2013
09/13

by
Volker Schomerus; Hubert Saleur

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We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit (``harmonic analysis on the supergroup''). Its spectrum is shown to contain indecomposable representations. This is interpreted as a geometric signal for the appearance of logarithms in the correlators of the full field theory. We then discuss the representation theory of the gl(1|1) current algebra and propose an Ansatz for the state space of the WZW...

Source: http://arxiv.org/abs/hep-th/0510032v1

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Jun 29, 2018
06/18

by
Mikhail Isachenkov; Volker Schomerus

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We observe that conformal blocks of scalar 4-point functions in a $d$-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled P\"oschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension $d$, is known to be superintegrable. Our observation enables us to exploit the rich mathematical literature on Calogero-Sutherland models in deriving various results for...

Topic: High Energy Physics - Theory

Source: http://arxiv.org/abs/1602.01858

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Sep 21, 2013
09/13

by
Henning Schomerus; Philippe Jacquod

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We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, tau_E becomes parametrically larger than the...

Source: http://arxiv.org/abs/cond-mat/0508092v1

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Jun 30, 2018
06/18

by
Henning Schomerus; Jan Wiersig

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Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such...

Topics: Physics, Mesoscale and Nanoscale Physics, Optics, Condensed Matter

Source: http://arxiv.org/abs/1409.5037

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Sep 18, 2013
09/13

by
A. Recknagel; V. Schomerus

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Boundary conformal field theory is the suitable framework for a microscopic treatment of D-branes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of D-branes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated...

Source: http://arxiv.org/abs/hep-th/9811237v2

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Sep 18, 2013
09/13

by
M. Titov; H. Schomerus

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We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results...

Source: http://arxiv.org/abs/cond-mat/0504057v2

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Sep 22, 2013
09/13

by
Christopher Birchall; Henning Schomerus

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We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics, and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted...

Source: http://arxiv.org/abs/1004.5298v1

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Sep 19, 2013
09/13

by
H. Schomerus; M. Titov

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We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in single-parameter scaling theory. A direct link to the break-down of the random-phase approximation is established. Our findings are confirmed by a parameter-free comparison to the results of numerical simulations.

Source: http://arxiv.org/abs/cond-mat/0208457v1

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Sep 21, 2013
09/13

by
Stefan Fredenhagen; Volker Schomerus

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In this note we discuss bound states of un- or meta-stable brane configurations in various non-trivial (curved) backgrounds. We begin by reviewing some known results concerning brane dynamics on group manifolds. These are then employed to study condensation in cosets of the WZW model. While the basic ideas are more general, our presentation focuses on parafermion theories and, closely related, N=2 superconformal minimal models. We determine the (non-commutative) low energy effective actions for...

Source: http://arxiv.org/abs/hep-th/0104043v1

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Sep 22, 2013
09/13

by
M. Hentschel; H. Schomerus

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We discuss curvature corrections to Fresnel's laws for the reflection and transmission of light at a non-planar refractive-index boundary. The reflection coefficients are obtained from the resonances of a dielectric disk within a sequential-reflection model. The Goos-H\"anchen effect for curved light fronts at a planar interface can be adapted to provide a qualitative and quantitative extension of the ray model which explains the observed deviations from Fresnel's laws.

Source: http://arxiv.org/abs/physics/0111160v1

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Sep 19, 2013
09/13

by
M. Titov; H. Schomerus

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Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wave length to the...

Source: http://arxiv.org/abs/cond-mat/0302580v1

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Sep 22, 2013
09/13

by
Volker Schomerus; Paulina Suchanek

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N=1 super Liouville field theory is one of the simplest non-rational conformal field theories. It possesses various important extensions and interesting applications, e.g. to the AGT relation with 4D gauge theory or the construction of the OSP(1|2) WZW model. In both setups, the N=1 Liouville field is accompanied by an additional free fermion. Recently, Belavin et al. suggested a bosonization of the product theory in terms of two bosonic Liouville fields. While one of these Liouville fields is...

Source: http://arxiv.org/abs/1210.1856v1

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Jul 20, 2013
07/13

by
Thomas Creutzig; Volker Schomerus

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We investigate correlation functions for maximally symmetric boundary conditions in the WZNW model on GL(1|1). Special attention is payed to volume filling branes. Generalizing earlier ideas for the bulk sector, we set up a Kac-Wakimoto-like formalism for the boundary model. This first order formalism is then used to calculate bulk-boundary 2-point functions and the boundary 3-point functions of the model. The note ends with a few comments on correlation functions of atypical fields, point-like...

Source: http://arxiv.org/abs/0804.3469v1

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Jul 20, 2013
07/13

by
A. Recknagel; V. Schomerus

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We discuss D-branes from a conformal field theory point of view. In this approach, branes are described by boundary states providing sources for closed string modes, independently of classical notions. The boundary states must satisfy constraints which fall into two classes: The first consists of gluing conditions between left- and right-moving Virasoro or further symmetry generators, whereas the second encompasses non-linear consistency conditions from world sheet duality, which severely...

Source: http://arxiv.org/abs/hep-th/9712186v2

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Sep 18, 2013
09/13

by
Andreas Recknagel; Volker Schomerus

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D-branes in curved backgrounds can be treated with techniques of boundary conformal field theory. We discuss the influence of scalar condensates on such branes, i.e. perturbations of boundary conditions by marginal boundary operators. A general criterion is presented that guarantees a boundary perturbation to be truly marginal in all orders of perturbation theory. Our results on boundary deformations have several interesting applications which are sketched at the end of this note.

Source: http://arxiv.org/abs/hep-th/9903139v1

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Sep 21, 2013
09/13

by
G. Mack; V. Schomerus

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Quantum field planes furnish a noncommutative differential algebra $\Omega$ which substitutes for the commutative algebra of functions and forms on a contractible manifold. The data required in their construction come from a quantum field theory. The basic idea is to replace the ground field ${\bf C}$ of quantum planes by the noncommutative algebra ${\cal A}$ of observables of the quantum field theory.

Source: http://arxiv.org/abs/hep-th/9403170v1

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Sep 22, 2013
09/13

by
S. Fredenhagen; V. Schomerus

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We propose a new rule for boundary renormalization group flows in fixed-point free coset models. Our proposal generalizes the 'absorption of boundary spin'-principle formulated by Affleck and Ludwig to a large class of perturbations in boundary conformal field theories. We illustrate the rule in the case of unitary minimal models.

Source: http://arxiv.org/abs/hep-th/0205011v1

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Sep 18, 2013
09/13

by
Hubert Saleur; Volker Schomerus

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Motivated by a careful analysis of the Laplacian on the supergroup $SU(2|1)$ we formulate a proposal for the state space of the $SU(2|1)$ WZNW model. We then use properties of $\hat{sl}(2|1)$ characters to compute the partition function of the theory. In the special case of level $k=1$ the latter is found to agree with the properly regularized partition function for the continuum limit of the integrable $sl(2|1) 3-\bar{3}$ super-spin chain. Some general conclusions applicable to other WZNW...

Source: http://arxiv.org/abs/hep-th/0611147v1

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Sep 23, 2013
09/13

by
Martin Sieber; Henning Schomerus

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We derive a uniform approximation for semiclassical contributions of periodic orbits to the spectral density which is valid for generic period-quadrupling bifurcations in systems with a mixed phase space. These bifurcations involve three periodic orbits which coalesce at the bifurcation. In the vicinity of the bifurcation the three orbits give a collective contribution to the spectral density while the individual contributions of Gutzwiller's type would diverge at the bifurcation. The uniform...

Source: http://arxiv.org/abs/chao-dyn/9708013v1